Answer:

Explanation:
a(t)=20t i+sin(t) j +cos(2t) k
v(t)=
=
---------------eqn 1
given v(0)=i
i=

from equation 1
V(t)=
----------eqn 2
now r(t)=

given r(0)=j
0i+1j+ok = 


As the plastic sphere is charged, therefore it experience an electric force when placed in an electric fields and also experiences gravitational force acts downward so the electric force must act upward.
Let
is electric force and
is gravitational force.
If these forces are balanced, therefore
or 
Given,
and
.
Substituting these values in above equation we get,

Thus, the magnitude of electric field is
.
As the charge is negative, the electric field at the location of the plastic sphere must be pointing downward.
Answer:
The x-coordinate of the particle is 24 m.
Explanation:
In order to obtain the x-coordinate of the particle, you have to apply the equations for Two Dimension Motion
Xf=Xo+Voxt+0.5axt²(I)
Yf=Yo+Voyt+0.5ayt² (II)
Where Xo, Yo are the initial positions, Xf and Yf are the final positions, Vox and Voy are the initial velocities, ax and ay are the accerelations in x and y directions, t is the time.
The particle starts from rest from the origin, therefore:
Vox=Voy=0
Xo=Yo=0
Replacing Yf=12, Yo=0 and Voy=0 in (I) and solving for t:
12=0+(0)t+ 0.5(1.0)t²
12=0.5t²
Dividing by 0.5 and extracting thr squareroot both sides:
t=√12/0.5
t=√24 = 2√6
Replacing t=2√6, ax=2.0,Xo=0 and Vox=0 in (I) to obain the x-coordinate:
Xf=0+0t+0.5(2.0)(2√6)²
Xf= 24 m
I don't see an image, but the force of gravity depends on mass and distance. If the mass and the distance are different, you divide (mass÷distance).the greater the number the greater the force of gravity.
Tell me if you need more info.
C. 76 I just did the question earlier